See also the
Dr. Math FAQ:
Browse High School Higher-Dimensional Geometry
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Do cones or cylinders have edges?
Latitude and longitude.
MaximizIng the volume of a cylinder.
- Changing Angle of a Tank [06/11/2003]
Points A and B represent pressure sensors in fixed positions on the
base of a round tank. The chord through CD represents the water level
in the tank. Lines a and b are the heights of water registered by each
- Cones, Pyramids: Surface Area and Volume Formulas [03/11/2003]
How do you get the formula for surface area and volume for cones and
- Coordinate Systems, Longitude, Latitude [04/19/1997]
Can you explain pitch, roll, and yaw to me? Are there other systems for
measuring an object's position in space?
- Does a Cone have an Edge? A Vertex? [03/12/2002]
Our 4th grade math textbook defines a cone as "A solid figure with one
circular face and one vertex." This sounds reasonable until you read the
textbook's definitions for face, edge, and vertex.
- Fourth Dimension [05/13/1997]
Can you help me understand the fourth dimension?
- HyperCubes [3/21/1996]
Do you folks know of any videos that show the hyper-cube in action that
would be appropriate for the high school level?
- Is a Sphere 2-D or 3-D? [8/8/1996]
Is a sphere a two- or a three-dimensional object?
- Number of Cylinder Edges [04/01/2002]
My son was asked "how many edges are there on a solid cylinder?" on a
recent math examination. His answer was "2" and it was marked incorrect.
- Three-dimensional Plane Diagrams [03/10/1999]
Draw: two parallel planes with another plane intersecting them; two
parallel planes with an intersecting line.
- Volume equations for a sphere and pyramid [6/10/1996]
I am now thoroughly confused: we just learned the formulas for volume of
a sphere and volume of a pyramid, but, he wouldn't tell me how to do it.
- Volume of a Pyramid [05/16/1999]
Can you give a step-by-step proof for the volume of a pyramid?
- 3D Figures and Intersections [03/04/1999]
Determining whether a line and plane intersect, and where, using vectors.
- 3D Geometry [11/17/1997]
You can draw a line of minimum distance between and perpendicular to two
lines in 3space. I know how to get the distance and direction of this
line, but I want to locate the line in 3space so that I can find its
- A 3-D Object that Fits 3 Holes [06/03/1999]
How can I make an object that can fit in 3 holes of different shapes,
blocking all light, and sliding all the way through without forcing it?
- 3-D Shape That Can Be a Circle, Square, or Triangle in 2-D [09/08/2006]
Is there a shape that can fill and pass through a circular hole, a
square hole, and a triangular hole?
- The 4th Dimension [2/10/1996]
In my Geometry class we read the book, Sphereland . I couldn't
visualize Overcubes and Overspheres. Even though I know we really
shouldn't be able to see 4D figures, just as 2D creatures can't visualize
3D creatures, is there any way you could describe an oversphere?
- Adding a 6-Inch Layer of Gravel [03/13/2003]
Your company is constructing a soccer field for a high school. The
field is 110 yards long and 80 yards wide...
- Angle Between Two Points on the Globe [7/17/1996]
Given their longitude and latitude, how can you determine the angle in
radians between two cities?
- Angle Between Two Sides of a Pyramid [10/29/1999]
How can I compute the angle formed by two sides of a frustrum of a
- Area and Volume of a Football [3/28/1995]
How would one find the area of a football? Or then again, how would one
find the volume of a football?
- Area and Volume of a Pear [6/4/1996]
How do you find the area and volume of a pear?
- Area and Volume of Cuboid [09/09/2002]
How can I find the new volume and surface area of a cuboid after its
volume has been reduced by 10%?
- Area of a Cone [11/5/1994]
What is the area of a cone when given the height and the angle at the
- Area of a Pentagonal Pyramid [11/16/1995]
I would like to know the area of a pentagonal pyramid. The dimensions of
the sides of the base are 5cm ea. and the height is 23cm.
- The Area of a Roof [05/18/2002]
How can I determine the area of a hipped roof for a building 100
feet long and 80 feet wide, with a pitch of 6/12, and 3 feet of
overhang for the eaves?
- Area, Volume of a Cone [6/4/1996]
What are the formulae to find the volume and area of a cone?
- Bases and Faces [12/05/2001]
I can't figure out the difference between a base and a face on the shapes
we are learning.
- Bearing Between Two Points [12/19/2001]
Is there an easy way to calculate the "heading" (relative to North=0)
between two coordinates?
- Bearing Calculation [09/01/1997]
Given two cities at geographic coordinates (xA,yA) and (xB,yB), is there
a formula to calculate the bearing from city A to city B?
- Beyond the Third Dimension [5/16/1996]
I am searching for information on 'beyond the third dimension'.
- Beyond Three-Dimensional Geometry [06/17/2001]
If the first dimension is a line and the second dimension is a flat
figure, the the third dimension is, say, a cube, then what is the fourth
dimension? What is the fifth dimension?
- Board Feet from a Log [03/19/2003]
What is the board feet of a 10-foot log if the diameter is 16 inches
at one end and 14 inches at the other end?
- Box for a Ball [09/26/2002]
The volume of a ball is 36pi cm^3. How do I find the dimensions of a
rectangular box that is just large enough to hold the ball?
- Bricks to Cover a Steeple [08/23/1997]
How many 6"x12" bricks would it take to cover an octagonal steeple with a
diameter of 130 ft. and a height of 370 ft?
- Building a Cone [01/28/2002]
I am trying to draw cone (frustum) with a larger radius size.
- Building a Cone [10/28/2001]
I am trying to find a formula for building a cone for a chimney flashing.
It should be 21" tall with a top opening of 8", a bottom opening of 20",
and a vertical seam overlap of 2".
- Building a Manger [12/03/2001]
Given a base of 11" and two walls 7 1/2' and 6" high, both meeting the
base a 90-degree angles, what is the length of the roof and what are the
angle measures where the walls meet the roof?
- Building a Skateboard Ramp [9/19/1995]
I'm trying to build a skateboard ramp, pyramid with flat top, height one
foot, angle of ascent thirty degrees, other angles ninety degrees and
- Building a Wooden Square-Based Pyramid [01/26/2001]
I want to build a wooden pyramid with a square base 8"by 8".
- CADAEIBFEC and Other NCTM Questions [10/27/1998]
CADAEIBFEC is a mnemonic for an important piece of mathematical
information. What is it?